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Dr. Sam Raskin
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Mathematics
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Spring 2016
Level
Graduate
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Algebra and Number Theory
Topology and Geometry
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18.786 | Spring 2016 | Graduate
Number Theory II: Class Field Theory
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Syllabus
Readings
Lecture Notes
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Lecture Notes
Artin and Brauer Reciprocity, Part I
Artin and Brauer Reciprocity, Part II
Brauer Groups
Chain Complexes and Herbrand Quotients
Derived Functors and Explicit Projective Resolutions
Exact Sequences and Tate Cohomology
GCFT and Quadratic Reciprocity
Hilbert Symbols
Homotopy Coinvariants, Abelianization, and Tate Cohomology
Homotopy, Quasi-Isomorphism, and Coinvariants
Introduction
Lectures on Cohomological Class Field Theory
Non-Degeneracy of the Adèle Pairing and Exact Sequences
Norm Groups with Tame Ramification
Norm Groups, Kummer Theory, and Profinite Cohomology
Proof of the First Inequality
Proof of the Second Inequality
Proof of the Vanishing Theorem
Tate Cohomology and Inverse Limits
Tate Cohomology and K[superscript unr]
The Mapping Complex and Projective Resolutions
The Vanishing Theorem Implies Cohomological LCFT
Vanishing of Tate Cohomology Groups
Hilbert’s Theorem 90 and Cochain Complexes
Course Info
Instructor
Dr. Sam Raskin
Departments
Mathematics
As Taught In
Spring 2016
Level
Graduate
Topics
Mathematics
Algebra and Number Theory
Topology and Geometry
Learning Resource Types
notes
Lecture Notes
assignment
Problem Sets
Download Course